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Popular Word Problems >

Sarah invested 53,000 in an account paying an interest rate of 4.5% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach 77,700?

Solution

S a r ah in v es t e d 53, 000 in an a cco u n t p a y in g an in t eres t r a t e o f 4.5% co m p o u n d e d d ai l y . A ss u min g n o d e p os i t s or w i t h d r a w a l s a re ma d e, h o w l o n g w o u l d i t t ak e, t o t h e n e a res t t e n t h o f a ye a r, f or t h e v a l u e o f t h e a cco u n t t o re a c h 77, 700 ?

Solution

Time : 8.5

Solution steps

Translate the problem into an equation:

77700 = 53000 (1 + \frac{0.045}{365})^{365 t}

Solve for

t, 77700 = 53000 (1 + \frac{0.045}{365})^{365 t} : t = 8.5

Time : 8.5

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