In most cases yes, you can do this. First I would recommend trying to get a small loan and see what happens. If they recommend that you have collateral first, offer your savings account. Your interest rate should be better and if that is an objective, offer it initially.
A few things you should be aware of. Many banks have a minimum loan amount. There is more cost for the bank than income when small loans are made so they look for a minimum amount which will be profitable for them. I've seen banks with minimum loan amounts in the range of $300 to $2,500. Their minimum is up to them.
They may ask that the savings account be converted to a Certificate of Deposit as they would rather have the CD as collateral than a general savings account.
Last, you should still earn interest on the CD, but the loan rate will be slightly higher with a 1% to 3% margin. That margin is the difference between what they pay you and you pay them. It represents their profit. Again, the rate they charge and any fees on the loan are up to the bank and to you.
You build up a credit history by borrowing and repaying money over time. I have seen borrowers repay a loan in 60 or 90 days and assume this built their credit up. It didn't as that was no demonstration that they could make payments month after month. Some borrowers would also ask that I "take this month's payment from the savings account." That doesn't build up credit either, at least not with me. It doesn't show that they can make payments back to me each month either.
If you ever have a problem making a payment, talk to the lender. They may have extension and renewal options to protect your credit and help you get over a rough time. Know for sure that construction of good credit takes time, destruction takes only a few months.
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